Selecting faces of "inside" of solidified surface
'Apply' has a specific meaning in the context of modifiers. In this case, it looks like you've only added the Solidify modifier and enabled edit-mode viewing. Since the base geometry is still a plane, the correct interpretation of it is to select both upper and lower faces produced from solidifying it.
To 'fix' this, all you need to do is apply the modifier --- producing a new base geometry. To do this in 2.8 and below, enter object mode and click the apply button on the modifier's card. In 2.90, this changed from being visible as a button to being an item on the drop-down menu to the right of the modifier's name. CTRL-A works as a shortcut when the mouse is over the modifier's card.